It requires some skill and practice to balance a rod standing upwards on the palm of one's hand. With the rotatory inverse pendulum, among other things, this challenge can be imitated. The system, here consisting of a pendulum (analogous to the rod), a driven swinging arm (our arm) and a base unit (our body), is nonlinear and in the upper equilibrium state (vertically upright pendulum) also unstable.

A challenge now is to design a controller that stabilizes the pendulum in the upper equilibrium state. Furthermore, challenges can be mastered like the swinging up of the pendulum from the lower equilibrium position (vertically hanging) to the upper one or a pendulum looping (360° rotation).

Condition of the Pendulum before and after Swinging up

The first photo shows the downward directed rod before swinging up, the second photo shows the state of the rod in the upper equilibrium state after swinging up.

a downward bar before the swing up
a rod pointing upwards after swinging up

Video: Swing up the Pendulum and Pendulum Looping

In this video you can see the pendulum swinging up from the lower equilibrium position and a pendulum looping (360° rotation).

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Video: Swinging up the pendulum

Challenges for the Teaching

  • Stabilization of the pendulum in upper equilibrium position
  • Stabilization during maneuvers (given swing arm rotations)
  • Robustness with respect to disturbances (attacking forces, motor voltage pulses)